DPIs in blender - How are they set up
Edit: As Duane points out in the comment below, DPI is often incorrectly used and PPI is more appropriate. It is very likely, however, that DPI and PPI are being used interchangeably in the context of OP's question.

DPI PPI means "Dots Pixels Per Inch." It is an expression of resolution over length and is most commonly used in printing. It is used to tell other software how far to spread out the pixels for printing.

For this to be meaningful in Blender, you'll need to know how large the final reproduction of the graphic will be on a page (or poster, or whatever you're making). The math is pretty straightforward:

Render X Resolution = Print Width * DPI PPI

Render Y Resolution = Print Height * DPI PPI

For example, if you were rendering for a 4 x 3 print, the render resolution would be 4*300 x 3*300 ==> 1200 x 900.

Be aware that the rendered file will carry a default DPI PPI definition of 72 or 96, but that only tells the Inkscape or Illustrator how large to make the picture on the page at import. Once you have your render, you can change the file's DPI PPI definition in GIMP or Photoshop without changing the actual pixel count. (Be aware that other softwares may be using DPI and PPI interchangeably.)